Irregular Tesselating Pentagon Type 6

Irregular Tesselating Pentagon Type 6
John Matz
11/13/2020
George Mason University
Math 401: Mathematics Through 3D Printing

This irregular pentagon is one of the fifteen pentagons that can seamlessly tile the infinite plane. Though this particular tile is concave or nonconvex, it is a type 6 pentagon, which is one of the pentagons that will tessellate as either a convex or concave type. According to Wikipedia, “Types 1, 2, 4, 5, 6, 7, 8, 9, and 13 allow parametric possibilities with nonconvex prototiles.”[1]

The Type 6 pentagon is one of three pentagon types (6, 7 & 8) discovered by Richard Kershner in 1968.[1] He believed that these were the last possible pentagonal tilings, but seven more types were subsequently discovered.[1] Only recently, in July 2017, did Michaël Rao successfully execute a computer-assisted proof that demonstrated that there were no remaining undiscovered convex pentagonal tile types.[1]

The Type 6 pentagon is differentiated from other pentagonal t